Open AccessInformal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability
Author(s) -
Pawel Pawlowski,
Rafał Urbaniak
Publication year - 2021
Publication title -
logic and logical philosophy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.416
H-Index - 10
eISSN - 2300-9802
pISSN - 1425-3305
DOI - 10.12775/llp.2021.016
Subject(s) - arithmetic function , mathematics , extension (predicate logic) , order (exchange) , algebra over a field , calculus (dental) , computer science , discrete mathematics , pure mathematics , programming language , medicine , dentistry , finance , economics
BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not.